In the chemical industry, it is important to effectuate precise prediction of properties of compounds. Several methods have been employed, including wet methods such as extraction. However, such methods have proven to be time consuming and yield low precision results. A typical method of determining properties has therefore been through instrumental analysis. In particular, the use of quantized energy states of matter through spectroscopy solves many of the efficiency problems involved in methods such as extraction.
Nuclear magnetic resonance (NMR) is a powerful spectroscopic technique for structural analysis which utilizes commonly found elements such as hydrogen and carbon as "chromophores." With the aid of NMR, it is possible to define the environment of practically all commonly occurring functional groups, as well as fragments (e.g., hydrogen atoms attached to carbon) that are not otherwise accessible to spectroscopic or analytical techniques.
The single most important application of NMR has been in the qualitative identification of organic compounds and the elucidation of their structure. However, NMR can also be used for quantitative determination of compounds in mixtures and hence for following the progress of chemical reactions. More sophisticated applications often yield kinetic and thermodynamic parameters for certain types of chemical processes; and others, in particular spin-spin coupling, often give accurate information about the relative positions of groups of magnetic nuclei within molecules.
One means of obtaining an NMR spectrum involves the application of a strong radio frequency (RF) pulse of energy over the whole range of frequencies while the magnetic field is kept constant. As a result, nuclei are flipped to their upper state from which, over time, they will return (decay) to the lower state. Collecting the thus-induced current as a function of time through a computer creates a time-domain signal, which is a generally complex pattern called the free-induction decay (FID). Interpretation of an FID is often difficult; however, a Fourier transformation of an FID performed on the same dedicated computer yields a spectrum virtually identical to the regular absorption spectrum. This type of spectroscopy is called Fourier transform (FT) spectroscopy and is mostly applied on "high resolution" instruments with high magnetic fields (i.e. 2-14 Tesla).
NMR instruments that are used for process purposes typically have very low magnetic fields (i.e. .about.0.5 Tesla). However, at such low magnetic fields, there are not enough energy differences between different types of nuclei to resolve them by FT, especially in analyzing solid samples. Therefore, the time domain signal, or FID, is the main source of information for low magnetic field instruments. However, interpretation of the FID data when using the NMR for industrial process analysis and control can be quite difficult. Prior art methods suggest solutions that involve various iterative techniques for interpreting and thereafter utilizing the FID curve to interpret properties of compounds. Such methods involve the use of large tables of data with a single equation for interpreting the FID curve or alternatively, construction of a mathematic model where the results of experiments are expressed as a mathematical function of the experimental conditions. The mathematical function method provides a means of predicting and estimating the results at levels that were not directly studied. The mathematical equation that expresses the results (e.g., solubility of inorganic salts) in terms of the experimental factors (e.g., temperature and ionic strength) is referred to as the model. The experimental results are referred to as the responses. For optimization purposes, such a model can be very crucial.
To construct the model, instrument responses from samples with known concentration levels are measured and a mathematical relationship is estimated which relates the instrument response to the concentration of the chemical component(s). This model may be used to predict the concentration of a chemical component in future samples using the measured instrument response(s) from those samples. Prior art applications such as U.S. Pat. No. 5,675,253 issued to Smith et al. ("Smith '253") discloses developing such a mathematical model. In particular, the patent discloses using a Marquardt-Levenberg (M-L) curve-fitting approximation technique to determine the magnitude of all the parameters that best fit the FID curves. Smith '253 further teaches a calibration procedure which compares known samples and curve-fit points using time function equations including Gaussians, exponentials, Abragrams (defined herein as Gaussian multiplied by the quantity sin (.infin.t) divided by .infin.t), modified exponentials (defined herein as Ce.sup.-z where C is a constant, z=(kt).sup..infin., and .infin. lies between 0 and 1 or 1 and 2), modified Gaussians (defined herein as Gaussian multiplied by the cosine of the square root of t), and trigonometrics. However, such a curve-fitting procedure decreases the accuracy of the model and thus the accuracy of the resulting prediction.
There is a continuing need in the industry for an improved on-line system of relating multiple responses from an instrument to a property or properties of a polymer to enhance the accuracy, precision, and efficiency of prediction.